Acoustics of Musical Instruments by Antoine Chaigne

By Antoine Chaigne

This e-book, the 1st English-language translation of Acoustique des tools de musique, moment Edition, provides the mandatory foundations for knowing the advanced actual phenomena considering musical tools. what's the functionality of the labium in a flute? Which beneficial properties of an software let us make a transparent audible contrast among a clarinet and a trumpet? With assistance from a variety of examples, those questions are addressed intimately. The authors concentration specifically at the major effects received within the box over the last fifteen years. Their objective is to teach that easy actual versions can be utilized with profit for varied purposes in sound synthesis, software making, and sound recording. The publication is basically addressed to graduate scholars and researchers; but it may be of curiosity for engineers, musicians, craftsmen, and song fanatics who desire to know about the fundamentals of musical acoustics.

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Some results presented here are summarized and detailed further in Chap. 5 where the dissipation effects are studied. Acoustic Quantities and Decibels The variation of the acoustic quantities is small, but its magnitude can vary considerably, by a factor 107 , from the lowest audible sound to the sound of a taking off airplane: this is the reason why the decibel scale is used. p=p0 /, where p0 is the reference value equal to 2 10 5 Pa. This value is almost the lowest sound level perceived by the ear at 1000 Hz.

This is also the case for the acoustic velocity. Therefore, in one dimension, the general solution for both the potential and velocity has an expression similar to Eq. 112). For the outgoing wave, we have @f C =@t D c@f C =@x, and we deduce p D cvx . The quantity p=v is the specific acoustic impedance, which, for p both waves, is called the characteristic impedance. It is equal to ZS D c D = S, 1 Continuous Models 39 p while c D 1= and S , is S . The pair of parameters of our fluid-spring system, equivalent to another pair, which characterizes a plane traveling wave: the speed of sound c and the specific characteristic impedance, or impedance of the medium, ZS .

The case of orthotropic plates is selected as an illustration. It is particularly useful in musical acoustics since it can be applied to wooden plates used in lutherie [13, 55]. x; y; t/. We assume that the coordinates coincide with the symmetry axes of the material and that ez is the transverse direction. 61) B yy C D B C 0 CB C B C B C @ A B1 xy yx 1 xy yx C@ A @ A " xy xy 0 0 2Gxy where the coefficients ij are such that 1 ij ji > 1 [13]. 65) 24 A. Chaigne and J. Kergomard The equation of motion is again obtained from the Hamilton integral [Eq.

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